Evie, I understand, I have felt that same way at church prayer meetings. Just like you, I pray with my kids and with the immediate family, at first it was a little bit awkward, but after a while, talking to God with others in prayer has gotten easier, I just keep my focus on God and not on the hearers.
Maybe it seems like it's more of a performance in front of others or something, but keep close to God, He knows your heart, even if you don't publicly pray eloquently.
Now, learning how to share your faith, especially with nonbelievers, is a skill every Christian should learn and overcome fear of man for. There are great resources to learn how to do that. Start with some tracts, and build your confidence by studying how to evangelize. We should all be sharing our faith, this corrupt world is going to hell, it is morally right to try to save souls and snatch from the fire. I am learning how to do this, God is graciously allowing me to so far evangelize to old friends and family through letter writing, I learned how to share the entire Gospel after listening to Kirk Cameron's preaching of "Soundly Saved" on Way of the Master web site. He teaches the whole Gospel in a way that completely makes sense to everyone (as God opens the understanding of the hearer). I am also giving tracts and bibles. One Christian from long ago says tracts are the first baby step to spreading the Gospel. I am totally on this step, I have shared the Gospel with several neighbors, and also with a door-to-door salesmen with the help of my mom, but mostly I give tracts. There are some really great ones around, find one you would feel comfortable giving away. A great one is "Are you good enough to go to heaven?" from Living Waters with Ray Comfort, an associate of Kirk Cameron's. It completely shows sinners what sin is, and what God intends to do about it (all liars will have their part in the lake of fire Rev 21:8, etc). Evangelism is such a great work to share God and to truly love your neighbors as yourself.